Problem: Solve for $x$ and $y$ using elimination. ${2x+3y = 20}$ ${-x+4y = 23}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $2$ ${2x+3y = 20}$ $-2x+8y = 46$ Add the top and bottom equations together. $11y = 66$ $\dfrac{11y}{{11}} = \dfrac{66}{{11}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {2x+3y = 20}\thinspace$ to find $x$ ${2x + 3}{(6)}{= 20}$ $2x+18 = 20$ $2x+18{-18} = 20{-18}$ $2x = 2$ $\dfrac{2x}{{2}} = \dfrac{2}{{2}}$ ${x = 1}$ You can also plug ${y = 6}$ into $\thinspace {-x+4y = 23}\thinspace$ and get the same answer for $x$ : ${-x + 4}{(6)}{= 23}$ ${x = 1}$